THE JOURNAL OF CHEMICAL PHYSICS 146, 092329 (2017)

Single-molecule force-conductance spectroscopyof hydrogen-bonded complexes

Alessandro Pirrotta,

1

Luca De Vico,

2

Gemma C. Solomon,

1

and Ignacio Franco

3,a)

1Nano-Science Center and Department of Chemistry, University of Copenhagen, 2100 Copenhagen Ø, Denmark2Department of Chemistry, University of Copenhagen, 2100 Copenhagen Ø, Denmark3Departments of Chemistry and Physics, University of Rochester, Rochester, New York 14627-0216, USA

(Received 31 October 2016; accepted 2 February 2017; published online 22 February 2017)

The emerging ability to study physical properties at the single-molecule limit highlights the dispar-ity between what is observable in an ensemble of molecules and the heterogeneous contributions ofits constituent parts. A particularly convenient platform for single-molecule studies are molecularjunctions where forces and voltages can be applied to individual molecules, giving access to a seriesof electromechanical observables that can form the basis of highly discriminating multidimensionalsingle-molecule spectroscopies. Here, we computationally examine the ability of force and conduc-tance to inform about molecular recognition events at the single-molecule limit. For this, we considerthe force-conductance characteristics of a prototypical class of hydrogen bonded bimolecular com-plexes sandwiched between gold electrodes. The complexes consist of derivatives of a barbituric acidand a Hamilton receptor that can form up to six simultaneous hydrogen bonds. The simulations com-bine classical molecular dynamics of the mechanical deformation of the junction with non-equilibriumGreen’s function computations of the electronic transport. As shown, in these complexes hydrogenbonds mediate transport either by directly participating as a possible transport pathway or by sta-bilizing molecular conformations with enhanced conductance properties. Further, we observe thatforce-conductance correlations can be very sensitive to small changes in the chemical structure ofthe complexes and provide detailed information about the behavior of single molecules that cannotbe gleaned from either measurement alone. In fact, there are regions during the elongation that areonly mechanically active, others that are only conductance active, and regions where both force andconductance changes as the complex is mechanically manipulated. The implication is that force andconductance provide complementary information about the evolution of molecules in junctions thatcan be used to interrogate basic structure-transport relations at the single-molecule limit. Publishedby AIP Publishing. [http://dx.doi.org/10.1063/1.4976626]

I. INTRODUCTION

In the quest for unambiguous evidence in support oragainst a hypothesis, modern spectroscopy often takes advan-tage of multidimensional strategies to resolve signals that canhave multiple causes in linear spectroscopies.1,2 This is doneby considering the response of a system to two or more externalstimuli that are applied simultaneously, as their correlation canoften resolve ambiguities in the interpretation of the responseof a system to a single probe.

At the single-molecule limit,3–12 a current topical chal-lenge is to implement multidimensional spectroscopies thatallow us to examine individual molecules with unprece-dented resolution. Such capabilities will considerably enhanceour ability to probe, understand, and ultimately control thebasic constituents of matter. A particularly convenient plat-form for multidimensional single-molecule spectroscopies aremolecular junctions9,13–15 where forces, light, and voltagescan simultaneously be applied to individual molecules. Herewe focus on measurements that investigate the correlationbetween the electrical and mechanical properties of single

a)ignacio.franco@rochester.edu

molecules in junctions (see, e.g., Refs. 16–29). In this class ofmeasurements, a molecular junction is mechanically deformedwhile measuring its conductance, or its conductance and theapplied force. Experimental techniques that have been devel-oped or adapted for this purpose include low temperature Scan-ning Tunneling Microscopy (STM),30–33 STM-break junc-tions,18,19,34,35 alpha measurements,36 and conductive probeatomic force microscopy (CP–AFM).28,37,38 The utility ofthis class of multidimensional spectroscopy relies on the factthat conductance and force can offer complementary infor-mation about the behavior of single molecules. Conductanceprobes the electronic structure and transport-determining inter-actions across the molecule, while force probes the molecularinteractions that govern mechanical stability.

In this paper, we computationally investigate the abilityof single-molecule force-conductance spectroscopy to probehost-guest molecular recognition events. As an exemplifyingcase, we focus on the force-conductance properties of theprototypical class of hydrogen-bonded complexes shown inFig. 1, consisting of a Hamilton-like receptor39,40 host anda barbituric acid derivative guest. This class of host-guestcomplexes have been previous employed in developing molec-ular sensors39,40 and self-assembly strategies.41–43 Similar

0021-9606/2017/146(9)/092329/9/$30.00 146, 092329-1 Published by AIP Publishing.

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FIG. 1. Scheme of a CP-AFM force-conductance spectroscopy setup (leftpanel) and of the hydrogen bonded host-guest complexes considered here(right panel). In these experiments, the cantilever-holder-to-surface distance(L) is controlled while the end-to-end molecular distance (⇠) thermally fluc-tuates. The force F = �k(⇠ + l0 � L) is measured by the deflection of thecantilever from its equilibrium position (⇠ + l0 � L), where l0 is the fixedlength of the tip and k is the cantilever stiffness. Simultaneously, the conduc-tance of the molecular junction is measured. The complexes computationallyinvestigated in this setup consist of a Hamilton-like receptor host (C1 andO1) and a barbituric acid derivative guest molecule (2) connected to the goldsurfaces of the CP-AFM via thiol-gold bonds. The dashed green lines showthe six hydrogen bonds anticipated in the complex, identified with the letters↵, �, and �.

complexes have been synthesized by Glockner.44 The com-plexes are thiol-terminated and assumed to be chemisorbedto macroscopic gold surfaces. Through this example, weassess the utility of the force-conductance spectroscopy toprovide information about the basic intermolecular interac-tions that govern supramolecular communication events thatare important in a variety of drug design, catalysis, and self-assembly applications. These simulations complement pre-vious studies by us45 investigating the force spectroscopyof these complexes and their complexation thermodynamics.They also complement conductance experiments that havedemonstrated that hydrogen bonds are involved in the elec-tron transfer through molecules20,46–51 and can sometimes bemore conductive than covalent bonds.52

Our simulations mimic the CP–AFM force–conductancespectroscopy setup (see Fig. 1). In it, a molecule is attachedby its ends to a macroscopic metallic surface and an AFM tipconnected to a cantilever. This distance between the surfaceand the cantilever-holder L is controlled, while the molec-ular end-to-end distance ⇠ fluctuates. The fluctuating forceF = �k(⇠ + l0 � L) is determined by measuring the deflectionof the cantilever (⇠ + l0 � L) with respect to its equilibriumposition L, where k is the cantilever stiffness and l0 is the fixedlength of the tip. As the molecule is pulled by increasing L, avoltage is applied and both the force on the molecule and thecurrent passing through it are measured. The simulations areperformed by combining classical molecular dynamics (MD)of the pulling with electron transport computations using thenon-equilibrium Green’s function method.

The manuscript is organized as follows: Section II summa-rizes the MD and electronic transport computational methodsemployed in the simulations, and the local current analy-sis used to establish structure-transport relations. Section IIIdiscusses the resulting force-conductance spectroscopy, its

sensitivity with respect to changes in the chemical structure,and the basic force-conductance behavior that is encoun-tered during junction evolution. In Sec. IV we summarize ourmain findings and discuss the potential of the approach as asingle-molecule multidimensional spectroscopy.

II. THEORETICAL METHODSA. Molecular dynamics

The classical molecular dynamics strategy and computa-tional setup employed to model the force-spectroscopy havebeen presented before.6,45 Briefly, the mechanical deforma-tion of the complexes was simulated in the canonical ensemble(NVT) at 300 K using a Nose-Hoover chain as a thermostat.53

The equations of motion were integrated using the modifiedBeeman’s algorithm54–56 with a 1 fs time step. The force fieldemployed was a modified MM357 (with the amide functionalgroup parameters from the MM3-PRO58) and a refined setof hydrogen bond parameters previously developed45 to accu-rately model hydrogen bonded interactions in the complexes inFig. 1. The MM3 force field is known to adequately capture ⇡-stacking interactions as required to describe the interactionsin the complexes.59 The MD simulations were carried outwith TINKER 6.2.60 The metal tip and surface were modeledimplicitly as impenetrable and rigid parallel surfaces via poten-tial restraints that confine the molecule to the region betweenthe two surfaces. The surfaces were chosen to be perpendicularto the pulling direction and placed at a distance ⇠.

The MD computational setup mimics an AFM force-spectroscopy experiment with a cantilever force constant ofk = 110 pN/Å along the pulling direction and rigid alongdirections perpendicular to the pulling. The force constantemployed is common for AFM cantilevers and softer thanthe elasticity of gold (800 pN/Å)36 such that the cantileverdeflection, and not the gold’s, is dominant during pulling. Inthe simulations, a zero-length tip (l0 = 0) is considered and theposition of the cantilever holder is modeled via a dummy atom.Along the pulling coordinate, the dummy atom is connectedvia a harmonic spring of stiffness k to one of the molecular ter-minal S atoms. The position of the other molecular end is fixedthroughout the simulation. The deflection of the harmonicspring from its equilibrium position (⇠ � L) is the simulationequivalent to the cantilever deflection and measures the forceF = �k(⇠ � L) exerted on the molecule during pulling. Thecomputational setup supposes that the molecule-gold contactsdo not migrate during the pulling.

The simulations were performed using a pulling speedof 5 ⇥ 10 6 Å/ps. At this speed, the average force-extensionisotherms during pulling and subsequent contraction of thecomplexes essentially coincide, indicating that the systembehaves reversibly and the simulation data are independentof the pulling speed.45 The total simulated MD time was12 µs.

Cluster analysis in Visual Molecular Dynamics (VMD)61

was used to determine the most significant conformations dur-ing the pulling. This analysis consists in calculating the rootmean square deviation (RMSD) of each structure for a givenrange of ⇠ with respect to an arbitrary reference (data were

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binned in 1 Å intervals). The structures were clustered withrespect to their RMSD, determining the likelihood of each.

B. Electron transport

Electron transport across the junction is supposed to be insteady state at each instant of time during the mechanical defor-mation and well characterized by Landauer coherent transport.Thus, for each MD snapshot, the electronic structure of the sys-tem was computed at the Density Functional Tight-Binding(DFTB)62 level and the energy dependent transmission of thecomplex was computed using non-equilibrium Green’s func-tion method (NEGF).63 Specifically, the electron transportcomputations were carried out using the DFTB+NEGF62,63

software using the auorg Slater-Koster parameters64 devel-oped for describing interactions between organic moleculesand gold. We note that due to the finite spatial extent of thebasis functions in DFTB, this method is likely to underestimatethe long range transmission for the non-covalently bondedcomplexes considered here.

The transmission at the Fermi energy (which is directlyproportional to the zero-bias conductance of the molecule)was computed for 500 randomly selected frames in each 0.1 Åbin from L = 12 Å – 23 Å. For this, explicit gold electrodeswere added to the MD snapshots and connected to the ter-minal thiols. Specifically, the guest and host molecules werechemisorbed on 4⇥ 4⇥ 6 atom cluster electrodes by remov-ing the thiol hydrogen atoms and placing the sulfur atoms onan fcc(111) hollow site at 2.41 Å distance from the electrodesurface. These gold-sulfur distances were held constant for allcalculations and chosen according to the literature.65 Fermienergy of gold was set to 4.6840 eV. The electronic temper-ature of the electrodes was set to 50 K for smearing the Fermifunctions and to ease convergence. The effect on the conduc-tance of changing the contact temperature from 0 K to 300K was found to be negligible (2%-8% change in log(G/G0)for a test set of configurations) with respect to the thermaldistribution of conductance values.

C. Local currents

To establish structure-transport relations, a local currentanalysis was performed as described in Ref. 66. In it, thecurrent is decomposed into inter-atomic contributions, whichoffers a measure of how much current passes through a particu-lar bond or atom-pair. In the computations, a symmetric 0.1 eVbias was applied in order to decompose the Landauer-Buttikercurrents into contributions from atomic pairs. Average localcurrents are obtained over 0.5 Å bins for each L during theelongation. For definitiveness, we only choose conformationsthat have a logarithm of the transmission within 25% of theaverage hlog(G/G0)iL.

III. RESULTS AND DISCUSSIONA. Summary of previous findings

In Ref. 45 we computationally investigated the force-extension (F L) isotherms of the host-guest complexes inFig. 1 and two other complexes. The F L curves of thesecomplexes exhibit peaks that signal conformational changes

during elongation, the most prominent of which is in the 60–200 pN range and corresponds to the force required to breakthe hydrogen bonds. These peaks in the F L curves werefound to be sensitive to relatively small changes in the chemicalstructure of the host molecule. In addition, to obtain thermody-namic insights into the supramolecular assembly, in Ref. 45 wereconstructed from the force data the Helmholtz free energyprofile along the extension coordinate and decomposed it intoenergetic and entropic contributions. The complexation wasfound to be energetically driven and entropically penalized,with the energy contributions overcoming the entropy penaltyand driving molecular recognition. Further, the molecularnanoconfinement introduced by the macroscopic surfaces inthis class of experiments was shown to significantly accentuatethe mechanical and energetic stability of the hydrogen-bondedcomplexes, thus enhancing the ability of the force spectroscopyto probe this type of molecular recognition events.

Results presented below augment this picture by offer-ing insights into the conductance behavior and the force-conductance correlations.

B. Force-conductance distributions during elongation

Histograms associated with the force-conductance spec-troscopy for complexes C and O are shown in Fig. 2. Thefigure shows how conductance and force are correlated dur-ing the pulling. While the force is plotted individually to theconductance, they are both plotted as a function of a commonvariable (the end-to-end molecular extension ⇠ or the surface-to-cantilever holder distance L). As such, these plots conveyadditional information that is not readily evident in 2D force-conductance histograms of the data (shown in Figs. S1, S2,and S3 in the supplementary material). The generated statis-tics for both force and conductance have been checked forconvergence. Sample probability distributions of log(G/G0)during the pulling are included in Fig. S4 of the supplementarymaterial.

Both force and conductance exhibit large scale fluctua-tions that are comparable to the average values, as is charac-teristic for single molecules and other systems that are not inthe thermodynamic limit (where fluctuations of observablesare negligible with respect to average values).67,68

The fluctuations in the force reflect conformationalchanges along the ⇠ coordinate, while the fluctuations inthe transport reveal transport-determining conformationalchanges within the thermal ensemble. The average behaviorof force and conductance is indicated by the lines in Fig. 2.In the case of conductance, two averages are shown as fol-lows: the logarithm of the average loghG/G0i (dashed lines)and the average of the logarithm hlog(G/G0)i (solid lines).While hlog(G/G0)i follows closely the most probable conduc-tance value, the average conductance is dominated by a fewconformations with high conductance properties. The conduc-tance of the minimum energy structure of both complexes isshown by a star in the figure. Note that the conductance prop-erties of the geometrically relaxed structure do not necessarilycoincide with the statistical averages, pointing out the impor-tance of taking into account geometrical fluctuations whenestablishing structure-function relations.

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FIG. 2. ((a) and (e)) Chemical structures and ((b) and (f))optimized molecular structures of complexes C and O invacuum. The hydrogen bond lengths in the ↵, �,� orderare reported in Å. ((c), (d), (g), and (h)) 2D histogramsof force and conductance versus the cantilever-surfacedistance L and versus the S-S atoms distance ⇠ for com-plexes C and O. The color bar indicates the number ofcounts in bins of dimension 0.1 Å ⇥ 5 pN and 0.1 Å⇥ 0.1 log(G/G0). At L and ⇠ larger than 20.0 Å, asignificant probability distribution of frames with zeroconductance (log(G/G0) �12) arises. The star showsthe conductance of the minimum energy structure of bothcomplexes, and the lines represent the average behavior.In the case of conductance, two averages are shown asfollows: the logarithm of the average loghG/G0i (dashedlines) and the average of the logarithm hlog(G/G0)i (solidlines).

The results below complement this picture by offer-ing insights into the conductance behavior and the force-conductance correlations.

C. Force-conductance averages

Complexes O and C (cf. Fig. 1) can form the same numberand type of hydrogen bonds but differ by the central ring ofthe host molecule 1 and its connection to its two pyridine-based arms. These slight chemical modifications change

the mechanical stability and conductance properties of thecomplex and lead to dramatically different force-conductanceproperties. These differences are discussed below in termsof the average behavior of the log(conductance) and forcemeasurements (Figures 3(a)–3(d)) together with molecularconformations (top panel of Figure 3) obtained from a clus-ter analysis of the MD trajectory. We focus on hlog(G/G0)i,as opposed to loghG/G0i, because it provides a good esti-mate of the most probable conductance in the statisticalensemble.

FIG. 3. Average force and log(conductance) versus L and⇠ for complex C ((a) and (b)) and complex O ((c) and (d))in the vicinity of the breaking point. The averages werecalculated over a bin of width 0.5 Å. (Top panel) Repre-sentative conformations at different molecular lengths ⇠during the MD. These structures were selected througha cluster analysis of the trajectory and they represent themost probable structure within 1 Å of ⇠ .

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1. Complex C

During elongation, complex C undergoes a confor-mational transition from a stacked compact structure(L ⇡ 12 – 16.5 Å, ⇠ ⇡ 12 – 16.5 Å, structure 1) to a hydrogenbonded structure (L ⇡ 16.5 – 19 Å, ⇠ ⇡ 16.5 – 18.5 Å, struc-tures 2, 3) and finally to a mechanically deformed and partiallyuncomplexed state (L > 19 Å, ⇠ > 18.5 Å, structure 4). Repre-sentative conformations are shown in the top panel of Figure 3.These three main conformational stages lead to three distinctregions in the force-conductance behavior of this molecule,labeled I, II, and III in Figure 3. Specifically, in region I, themost probable conductance decays exponentially while theforce is approximately constant. In region II, the conductanceremains approximately constant while the force increases asthe hydrogen-bonded conformation is mechanically deformed.In region III, the force reaches its global maximum value andeventually drops. The peak in the force corresponds to theforce required to break the hydrogen bonds in the molecule.45

At this stage of the extension, all hydrogen bonds and anyother intermolecular interactions holding the complex togethercollectively break. This mechanical deformation and even-tual rupture of the complex leads to a sharp conductancedecay.

Note that the deformation and breaking of the gold con-tacts observed in related experiments69 that can give rise toadditional peaks in the force typically occur at larger forces(⇠1 nN) than the molecular events studied here.

2. Complex O

During pulling, complex O undergoes a conformationaltransition from a V shaped stacked molecule (10) to a hydrogenbonded structure (20, 30) and, subsequently, to an uncomplexedor partially complexed state (40). For this complex, we can alsoidentify three main regions in its force-conductance behavior.In region I (L ⇡ 12 – 18 Å, ⇠ ⇡ 12 – 17.6 Å), the force remainsapproximately constant and fluctuates around zero, while themost probable conductance observes exponential growth andreaches its maximum. The maximum in the conductance isachieved when the molecule is planar and thus can form thelargest number of intermolecular hydrogen bonds. In regionII (L ⇡ 18 – 21.7 Å, ⇠ ⇡ 17.6 – 20 Å), the force increases asthe fully formed hydrogen bonded complex is mechanicallydeformed. The mechanical weakening of the complex leadsto a decay in the conductance. Last, in region III (L > 21.7 Å,⇠ > 20 Å) the complex is mechanically broken leading to anabrupt decrease in both force and conductance.

3. Contrasting the two cases

In spite of their chemical similarities, the force-conductance spectroscopy of complexes O and C are quitedifferent. First, the force required to break the hydrogen bondsin complex O (205 pN) is approximately a factor of twolarger than the breaking force for complex C (89 pN). Thisis because, in its planar hydrogen bonded conformation, com-plex O forms, on average, 2-2.5 times more hydrogen bondsthan complex C.45 Further, the magnitude of the conductanceof complex O is much smaller than the one of complex C. Asdiscussed in Sec. III D, this is due to the limited electroniccoupling from the electrodes into the arms of O1 because of

the meta-substitution. Because of this, none of the hydrogenbonds in O can couple to the electrode and that considerablyreduces the transmission at the Fermi energy.70 In addition,the force-conductance correlations in the two complexes arequalitatively different. While in both cases region I is conduc-tance active but mechanically (approximately) inactive, forcomplex O stretching the stacked conformation leads to anincrease of the conductance, while the opposite is observedfor complex C. Region II is mechanically active in both cases,but it is only conductance active in complex O. In regionIII, in both cases the uncomplexation leads to a decay ofboth force and conductance. This qualitative and quantitativedependence of the force-conductance correlations to the chem-ical details makes this type of spectroscopy a powerful avenuefor single-molecule characterization.

Such differences in the conductance behavior of the twocomplexes are examined below via an analysis of the localcurrents.

D. Hydrogen bonds and local currents

While there is no through-bond pathway from one elec-trode to the other in our complexes, hydrogen bonded systemsare known to be able to carry current.49,51,52,71 However, hydro-gen bonds are not the only interactions that hold the complextogether, we have also ⇡–⇡ stacking interactions and van derWaals interactions. So, we are left with the following ques-tions: (1) Are the hydrogen bonds the dominant pathway(s)for carrying the current? (2) Is the magnitude of the currentcorrelated with the number of hydrogen bonds formed? Asdiscussed below, in complex C the conductance is mediatedby some of the hydrogen bonds, while in complex O thereis no correlation between hydrogen bond interactions and theconductance pathway. This difference in transport mechanismand the relative magnitudes of transport of the stacked vs. thehydrogen bonded conformations is the origin of the qualitativedifferences in the conductance behavior of these chemicallysimilar complexes during elongation.

To address the question of the conduction pathway, weexamine the average local currents through these systems andthe important hydrogen bonds. In Figs. 4–6, local currents(LCs) are depicted with red arrows on one representative struc-ture from the ensemble of conformations. The width of eacharrow is directly proportional to the relative contributions tothe current and normalized with respect to the largest elementobserved. Only LC elements greater than 2% of the total cur-rent are shown. To clarify the contributions of hydrogen bondsto the molecular conductance, we define a quantity analogousto the local currents that we call “hydrogen bond fractions”(HBFs). The HBFs are defined as the quotient of the averagehydrogen bond binding energy (HBBE) between a given pairof atoms with the largest HBBE possible for that particular HBtype (i.e., for O��H 3.5 kcal/mol and N��H 14 kcal/mol).45 Allpossible hydrogen bonds have been considered over the sameset of molecular conformations that were analyzed for the LCs.These HBFs are plotted with green lines in the same way aswas done for the LCs. The width of lines is directly propor-tional to the HBBE magnitudes. Only HBFs greater than 10%of the maximum HBBE are shown.

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FIG. 4. Complex C: Average hydrogenbond fractions (left, green lines) andlocal currents (right, red arrows) at dif-ferent L. To obtain averages, 50 conform-ers were randomly selected from the MDtrajectory over a 0.5 Å bin in L with theonly criterion that the log-conductanceof the conformer was within 25% of theaverage hlog(G/G0)iL . Both local cur-rents and relative hydrogen bonds werecalculated for each frame and the aver-age was plotted on one of the frames.The width of the arrows (lines) is directlyproportional to the relative magnitude ofthe inter-atomic local currents (hydrogenbond interactions). Note that the largecurrents observed in some frames in thefive-membered ring are predominantlyring currents that are not contributing tothe net current.

Figures 4 and 5 show the LCs and HBFs for complexesC and O, respectively, at different points during the extension.When plotting average LCs and HBFs on a fixed conforma-tion, there are interactions between atoms at large (apparentlyunphysical) distances. The reason for this is because a wholeensemble of conformations was taken into account to obtainaverages. To this extent, long range HBFs or LCs should beinterpreted as giving a measure of the conformational free-dom of the structure. In this discussion, we will employ the↵, �, � convention for the hydrogen bonds specified in Fig. 1.We will refer to the specific hydrogen bond formed by the ith(i = ↵, �, �) donor H atom and the jth (j = ↵, �, �) accep-tor atom as the iD-jA-HB. For example, a hydrogen bondbetween the amino group (NH2) of molecule 1 and the central��N��(C==O)��N��carbonyl of molecule 2 will be denoted as�D-↵A-HB.

1. Complex C

As can been gleaned from Figure 4, generally, for complexC the LCs and the HBFs involve the same atoms. While thereare atomic pairs that are not hydrogen bonded that are involved

in the current, and hydrogen bonded pairs that do not carrycurrent, the overall transport pathways approximately matchwith the important hydrogen bonded contributions in thismolecule for all extensions L considered. This suggests that,for this complex, in regions II and III transport is determinedby transport through hydrogen bonds.

In additional detail, for complex C at L = 12.25 Å only the�-HB and a ↵D-�A-HB are formed. The LCs show that onlythe ↵D-�A-HB carries current. Upon stretching, additionalhydrogen bonds form (L = 14.25 Å). Specifically, the guestmolecule shuttles between the two pyridine based arms (notethe two �-HBs form with both NH groups of the guest). Theelectron transport is still dominated by the ↵D-�A-HB. At L= 16.25 Å, a conformation close to the fully hydrogen bondedhost-guest complex forms and the current is now injected intothe central carbonyl of the guest (through the ↵-HBs). Thedrop in conductance can be explained by the different conduc-tion paths in the guest molecule (cf. Figure 4(a) with Figure4(c)). At L = 18.25 Å, two more hydrogen bonds are formed,however the conductance remains unchanged and the LCsindicate no change in the pathway. In the stretched host-guest

FIG. 5. Complex O: Average hydrogen bond fraction(left, green lines) and local currents (right, red arrows)at different L. The averaging procedure is described inFig. 4.

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FIG. 6. Representative structures, average relative hydrogen bonds (left,green lines), and local currents (right, red arrows) for complex O in its bistableform around L = 13.75 Å.

complex conformation at L = 20.25 Å, we find an asymmetry inthe hydrogen bonds, specifically the upper pyridine based arm(Figure 4(e)) forms stronger or more frequent hydrogen bonds(larger average of HBBEs) than the lower arm. Remarkably thesame is also found for the LCs demonstrating that the largerthe HBFs, the larger the LCs (albeit not the total current) forthis complex. Finally, at longer L the complex breaks and fewbinding interactions occur (↵A-�D-HB and �-HB).

While the local currents only show us where the currentactually flows, rather than giving us the reason why other pathsare not favored, we can use this information to ask questionsabout the potential limitations of alternant paths. In the caseof the three sets of hydrogen bonds, we can hypothesize thatthe dominant role of the ↵-HBs in carrying the current is dueto the absence of meta-substituted rings in the tunneling pathfor these HBs, a condition that is not fulfilled for the �-HB or�-HB pathways.

As a separate test of the observation that hydrogen bondsdirectly participate as a possible transport pathway in com-plex C, Figure 7 shows a 2D histogram of the hydrogenbond mediated intermolecular interactions and the conduc-tance, using conformations taken just before the peak in theforce-conductance isotherm (around ⇠ = 18 Å). As discussedin Ref. 45, this set of conformations is stabilized by hydrogenbonds. The lines in the plot correspond to the hlog(G/G0)i fordifferent interaction strengths. As shown, the conductance is

FIG. 7. 2D Histograms of the intermolecular hydrogen bonding interactions(HB energy) versus conductance for (a) complex C and (b) complex O forhydrogen bond stabilized structures (around ⇠ = 18 ± 0.5 Å). The color barindicates the number of counts in bins of dimension 0.5 kcal/mol ⇥ 0.1log(G/G0). The solid lines indicate the average log(G/G0) for varying degreesof HB energy. Note how in complex C the conductance is partially correlatedto the degree of hydrogen bonding, while in complex O it is independentof it.

partially correlated with the hydrogen bonding interactions. Infact, the distribution in the 2D histogram is diagonally skewed(this fact is evident both in the distribution and in the averages)indicating that the stronger the hydrogen bonding interactionsthe higher the conductance. Note that the correlation is notperfect as not all of the hydrogen bonds that can be formedparticipate in the current.

2. Complex O

As evidenced by Figure 5, and in contrast to complex C,during the extension of complex O the transport is not deter-mined by hydrogen bonds but by the overlap of the ⇡ system ofthe benzene ring (host) with the ⇡ system of the guest. Specif-ically, the transport between the two molecules is determinedby the electronic coupling between the benzene ring of thehost and the central carbonyl of the guest molecule, which arenot hydrogen bonded. In this case, the conductance increaseswith elongation as the V-shaped complex planarizes becausea planar structure leads to a stronger overlap between the two⇡-systems. After L = 18.25 Å, the molecules are pulled apartand the conductance decreases upon further stretching.

In additional detail, at L = 12.25 Å four hydrogen bondsparticipate of the dynamics: two ↵ and two �-HBs. As thecomplex is stretched, no hydrogen bonds are broken; the guestand host molecule pivot in opposite directions around the two�-HBs allowing the formation of the two �-HBs. Through-out the whole pulling process, the conductance is mediatedby the ⇡-systems of the donor and acceptor. The conductanceincreases upon stretching (from Figs. 5(a)–5(d)), reaching itsmaximum value at L = 18.25 Å. At this L the fully hydrogenbonded structure is reached. Thus, in this case, while hydro-gen bonds do not actively participate in the current they dostabilize a conformation where the orbital overlap betweenthe donor and acceptor enhances transport. This conclusionis also evident in Fig. 7, that shows that for complex O theconductance is uncorrelated with the strength of the hydrogenbonding interactions for conformations around ⇠ = 18 Å thatare stabilized by hydrogen bonds.

Figures 2(g) and 2(h) show a bistability in the conduc-tance for complex O at L (⇠)⇡ 14 Å. This bistability arisesbecause there are two distinct ensembles of conformationsthat have a conductance difference of two orders of magnitude.Figure 6 shows representative structures and the LCs and HBFsfor these two sets. As shown, this difference arises because inthe conformers of higher conductance the tunneling path issignificantly shorter due to the relative position of the guestand host molecules.

IV. FINAL REMARKS

In this paper, we have numerically investigated theforce-conductance signatures of molecular recognition eventsthrough hydrogen bonding, using the supramolecular complexshown in Fig. 1 as an exemplifying case. The simulations indi-cate that force-conductance correlations can provide detailedinformation about the behavior of single molecules that cannotbe gleaned from either measurement alone. This is becauseforce and conductance are complementary techniques; con-ductance probes the electronic structure of the molecule in

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a junction, while force-measurements probe the intramolecu-lar and intermolecular interactions which are responsible formechanical stability. Further, while force-spectroscopy allowsfor mechanical control over molecular conformation withsub-Angstrom resolution, conductance measurements permitmonitoring with exponential sensitivity transport-determiningchanges in conformation. Such exponential sensitivity arisesfrom the fact that electron transport through small moleculesoccurs through quantum mechanical tunneling.

The supposition in the simulations is that the transport iswell described by the Landauer formula. In any conformation-ally flexible system, incoherent transport may also be presentand can contribute to the overall current. Thus, the reportedconductances should be interpreted in a qualitative sense. Theyserve as a proxy to investigate the general question of whetherthe interactions that favor binding necessarily also favor trans-port. Landauer transport gives a simple picture of the electroniccoupling between the leads across the molecule and it is theevolution of this coupling that we probe.

Our view is that force-conductance measurements havethe potential to become a useful multidimensional single-molecule spectroscopy. In fact, in the case of the complexesconsidered, there were clear regions in the elongation thatare only mechanically active, others that are only conduc-tance active, and regions where both force and conductancechange as the complex is mechanically manipulated. In addi-tion, we find that elongating the supramolecular complex with-out breaking it can either increase (complex O) or decrease(complex C) the most probable conductance value. Further,bistable conductance regimes can be seen in regions wherethe force does not exhibit bistability. The implication of thisseries of observations is that force and conductance are sensi-tive to different types of changes in molecular conformationand, together, provide a richer understanding of the behaviorof single molecules in junctions.

Further, we have observed that force-conductance spec-troscopy can be very sensitive to details in the chemicalstructure. In fact, while the two complexes studied here areseemingly very similar, small changes in the structure canhave both qualitative and quantitative impact on the force,the conductance, and the force-conductance correlation. Atthe qualitative level, at least three different regions have beenidentified in the two complexes considered here from the trendof force and conductance upon elongation (Fig. 3). We canexpand these findings by taking into account all possible com-binations of how a change in molecular conformation can givea specific trend in the force or conductance signal under elon-gation. Figure 8 shows all these combinations: @F/@L and@ log G/@L equal, greater, or smaller than zero. An equiva-lent diagram can be made using the molecular elongation ⇠as a variable. For instance, case 4 vs. case 6 was observed inregion I for complex C vs. complex O; case 1 vs. case 2 inregion II. Other combinations could be measured in differentmolecules, and each one tells a different molecular story of thejunction evolution.

While Fig. 8 highlights the changing contributions of thetwo signals in a particular region, it is clear that the observedsequence of regions also provides additional information. Ina theoretical study such as this, it is generally possible to

FIG. 8. Different scenarios of the force and conductance trend versus thepulling coordinate. The dashed axes correspond to the derivative of force andconductance, respectively. Nine possible cases are shown and where possiblethe case is linked to the results shown in Fig. 3.

backtrack from the calculated observable to the atomisticdetails and rationalize the structure-function relationships thatare observed. In an experiment, however, the details of thestructural evolution of a flexible system under strain will gen-erally be unknown. It remains to be seen whether the combina-tion of changing force and conductance data will be sufficientto identify the structural motifs observed during a pullingexperiment, but there seems to be scope to expect a charac-teristic fingerprint from families of molecules as the systemmoves between regions in Fig. 8.

In the context of supramolecular complexes, an advan-tage of this type of spectroscopy is that the nanoconfinementof the molecular system between the AFM tip and the sur-face enhances the mechanical stability and the complexationenergy of the dimer.45 That is, nanoconfinement enhances thesensitivity of the force-conductance spectroscopy to molecu-lar recognition events. In the complexes considered, hydrogenbonds were seen to mediate transport either by directly par-ticipating as a possible transport pathway as revealed by localcurrents and energetic considerations (complex C), or by sta-bilizing molecular conformations with enhanced conductanceproperties (complex O).

Naturally, there are challenges that need to be overcometo further advance this route for multidimensional single-molecule spectroscopy. A basic experimental challenge is thelack of control of the junction configuration in break-junctionexperiments. This uncertainty in the conformation typicallyleads to an analysis based on statistical averages that do notnecessarily reflect the behavior of single molecules. From asimulation perspective, a significant challenge is how to over-come the 6-10 orders of magnitude gap between the pullingspeeds that are employed in experiments (nm/s) with thosethat can be achieved in silico. In spite of these challenges,this type of measurements provides a powerful avenue forthe manipulation and interrogation of basic chemical and

092329-9 Pirrotta et al. J. Chem. Phys. 146, 092329 (2017)

physical events, such as chemical reactions, molecular recog-nitions, and conformational dynamics.

SUPPLEMENTARY MATERIAL

See supplementary material for 2D force-conductancehistograms of the data.

ACKNOWLEDGMENTS

This work was supported by the University of Rochesterstartup funds. A.P., L.D.V., and G.C.S. acknowledge financialsupport from the Danish Council for Independent Research,Natural Sciences and the Carlsberg Foundation. A.P. thanksGabriele Penazzi for helpful conversations and comments.

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